Sparse Block-Jacobi Matrices with Exact Hausdorff Dimension

Abstract

We show that the Hausdorff dimension of the spectral measure of a class of deterministic, i. e. nonrandom, block-Jacobi matrices may be determined exactly, improving a result of Zlatos (J. Funct. Anal. 207, 216-252 (2004)).

22 pages

References in corpus (1)

• Eigenfunctions, transfer matrices, and absolutely continuous spectrum of one-dimensional Schrodinger operators

Cited by in corpus (2)

• On the uniform distribution of the Prüfer angles and its implication to a sharp spectral transition of Jacobi matrices with randomly sparse perturbations
• Pointwise Decay of Fourier-Stieltjes transform of the Spectral Measure for Jacobi Matrices with Faster-than-Exponential Sparse Perturbations